### Abstract

Manin's conjecture predicts an asymptotic formula for the number of rational points of bounded height on a smooth projective variety X in terms of global geometric invariants of X. The strongest form of the conjecture implies certain inequalities among geometric invariants of X and of its subvarieties. We provide a general geometric framework explaining these phenomena, via the notion of balanced line bundles, and prove the required inequalities for a large class of equivariant compactifications of homogeneous spaces.

Original language | English (US) |
---|---|

Pages (from-to) | 6375-6410 |

Number of pages | 36 |

Journal | International Mathematics Research Notices |

Volume | 2015 |

Issue number | 15 |

DOIs | |

State | Published - 2015 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*International Mathematics Research Notices*,

*2015*(15), 6375-6410. https://doi.org/10.1093/imrn/rnu129

**Balanced Line Bundles and Equivariant Compactifications of Homogeneous Spaces.** / Hassett, Brendan; Tanimoto, Sho; Tschinkel, Yuri.

Research output: Contribution to journal › Article

*International Mathematics Research Notices*, vol. 2015, no. 15, pp. 6375-6410. https://doi.org/10.1093/imrn/rnu129

}

TY - JOUR

T1 - Balanced Line Bundles and Equivariant Compactifications of Homogeneous Spaces

AU - Hassett, Brendan

AU - Tanimoto, Sho

AU - Tschinkel, Yuri

PY - 2015

Y1 - 2015

N2 - Manin's conjecture predicts an asymptotic formula for the number of rational points of bounded height on a smooth projective variety X in terms of global geometric invariants of X. The strongest form of the conjecture implies certain inequalities among geometric invariants of X and of its subvarieties. We provide a general geometric framework explaining these phenomena, via the notion of balanced line bundles, and prove the required inequalities for a large class of equivariant compactifications of homogeneous spaces.

AB - Manin's conjecture predicts an asymptotic formula for the number of rational points of bounded height on a smooth projective variety X in terms of global geometric invariants of X. The strongest form of the conjecture implies certain inequalities among geometric invariants of X and of its subvarieties. We provide a general geometric framework explaining these phenomena, via the notion of balanced line bundles, and prove the required inequalities for a large class of equivariant compactifications of homogeneous spaces.

UR - http://www.scopus.com/inward/record.url?scp=84939632761&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84939632761&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnu129

DO - 10.1093/imrn/rnu129

M3 - Article

AN - SCOPUS:84939632761

VL - 2015

SP - 6375

EP - 6410

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 15

ER -